Finding angle and magnitude

In an assembly operation, a robot moves an object first straight upwards and then to the east, around an arc forming on quarter of a circle of radius 4.80 that lies in an east-west vertical plane. The robot then moves the object upward and to the north, through a quarter of a circle of radius 3.70 cm that lies in a north south vertical plane. Find a) the magnitude of the total displacement of the object, and b) the angle the total displacement makes with the vertical.

Solution Preview

Suppose the original position is (0,0,0), we call it point O. During first period movement, it passes quarter of a circle ...